Jim wants to fence a rectangular pen for his chickens. The length of the pen should be at 78 feet and the perimeter should be no more than 412 feet. Which system of inequalities represent the possible dimensions of the pen?(1 point)%0D%0AResponses
Let's assume the width of the pen is 'w'.
The length is given as 78 feet, so we have the inequality:
length ≤ 78
The perimeter of a rectangle is given by the formula:
perimeter = 2*(length + width)
The perimeter is given as no more than 412 feet, so we have the inequality:
perimeter ≤ 412
Now, substituting the values and variables, we have the system of inequalities:
78 + w + 78 + w ≤ 412
Simplifying, we get:
2w + 156 ≤ 412
Subtracting 156 from both sides, we have:
2w ≤ 256
Dividing both sides by 2, we get:
w ≤ 128
So the system of inequalities that represent the possible dimensions of the pen is:
length ≤ 78
w ≤ 128